Title :
Design and analysis of a general recurrent neural network model for time-varying matrix inversion
Author :
Zhang, Yunong ; Ge, Shuzhi Sam
Author_Institution :
Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore
Abstract :
Following the idea of using first-order time derivatives, this paper presents a general recurrent neural network (RNN) model for online inversion of time-varying matrices. Different kinds of activation functions are investigated to guarantee the global exponential convergence of the neural model to the exact inverse of a given time-varying matrix. The robustness of the proposed neural model is also studied with respect to different activation functions and various implementation errors. Simulation results, including the application to kinematic control of redundant manipulators, substantiate the theoretical analysis and demonstrate the efficacy of the neural model on time-varying matrix inversion, especially when using a power-sigmoid activation function.
Keywords :
control system synthesis; convergence; matrix inversion; neurocontrollers; recurrent neural nets; redundant manipulators; stability; time-varying systems; transfer functions; activation functions; first-order time derivatives; global exponential convergence; implicit dynamics; inverse kinematics; kinematic control; neural model; online inversion; power-sigmoid activation function; recurrent neural network model; redundant manipulators; time-varying matrices; time-varying matrix inversion; Analytical models; Concurrent computing; Convergence; Cost function; Hardware; Kinematics; Neural networks; Recurrent neural networks; Robustness; Signal processing algorithms; Activation function; implicit dynamics; inverse kinematics; recurrent neural network (RNN); time-varying matrix inversion; Algorithms; Computer Simulation; Models, Theoretical; Neural Networks (Computer); Numerical Analysis, Computer-Assisted; Time Factors;
Journal_Title :
Neural Networks, IEEE Transactions on
DOI :
10.1109/TNN.2005.857946
